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Question

If $$\alpha$$ and $$\beta$$ are zeros of quadratic equation $$f(x)=x^2-px+q$$, then find the values of the following:
$$\alpha^2 +\beta^2$$


Solution

Given $$\alpha$$ and $$\beta$$ are zeros quadratic equation $$f(x)=x^2-px+q$$
$$\therefore \alpha +\beta =-\left( \dfrac {-p}{1}\right)=p$$
and $$\alpha =\dfrac q1=q$$
$$\alpha^2+\beta^2=(\alpha +\beta )^2-2\alpha \beta$$
$$=p^2-2q$$

Mathematics

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